Theoretical Probability Statistics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Two fair six-sided dice are rolled. What is the theoretical probability that the sum is 7?

Solution

  1. 1
    Step 1: The favourable outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), so there are 6 favourable outcomes.
  2. 2
    Step 2: There are 6×6=366 \times 6 = 36 equally likely outcomes in total, so the probability is 636=16\frac{6}{36} = \frac{1}{6}.

Answer

16\frac{1}{6}
Theoretical probability uses the full sample space of equally likely outcomes. Listing combinations carefully helps avoid missing or double-counting outcomes.

About Theoretical Probability

Theoretical probability is the expected probability of an event calculated by mathematical reasoning about equally likely outcomes, without conducting experiments. It equals the number of favorable outcomes divided by the total number of possible outcomes.

Learn more about Theoretical Probability →

More Theoretical Probability Examples

Example 1 medium

Two fair coins are tossed. Find the theoretical probability of getting exactly one head.

Example 2 medium

A fair die and a fair coin are used together. What is the probability of rolling a 3 AND getting hea

Example 3 medium

A bag has 4 red and 6 blue balls. One ball is drawn, replaced, and a second is drawn. What is the pr

← All Theoretical Probability Examples Theoretical Probability Concept